Hippocampal estimation of the random linear regression model used to estimate the effect of blood sugar on the size of red blood cells

Abstract

The regression model with a random explanatory variable is one of the widely used models in representing the regression relationship between variables in various economic or life phenomena, this model is called the random linear regression model. In this model, the different values of the explanatory variable occur with a certain probability, rather than being fixed in repeated samples. Therefore, it contradicts one of the basic assumptions of the linear regression model, which leads to the least squares estimators losing some or all of their optimal properties, depending on the nature of the relationship between the random explanatory variable and the random error terms. As an alternative to the ordinary least squares method, the modified maximum likelihood method (MMLE) was used, which was previously used by many researchers in estimating the coefficients of the random regression model, two methods have also been employed, which were used in estimating linear regression models that suffer from some standard problems, or if the sample values contain outliers or extreme values, these two methods are the MM method and the robust empirical likelihood method. The three methods are among the robust estimation methods. The aforementioned robust estimation methods were used to estimate the regression relationship between red blood cell volume (PCV) as a response variable and blood sugar (RBS) as a random explanatory variable based on the data of a random sample of 30 patients with heart disease. The results of the practical application revealed the superiority of the modified maximum likelihood method for the data of the research sample